/* * srfft.c * * Copyright (C) Yuqing Deng - April 2000 * * 64 and 128 point split radix fft for ac3dec * * The algorithm is desribed in the book: * "Computational Frameworks of the Fast Fourier Transform". * * The ideas and the the organization of code borrowed from djbfft written by * D. J. Bernstein . djbff can be found at * http://cr.yp.to/djbfft.html. * * srfft.c is free software; you can redistribute it and/or modify * it under the terms of the GNU General Public License as published by * the Free Software Foundation; either version 2, or (at your option) * any later version. * * srfft.c is distributed in the hope that it will be useful, * but WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the * GNU General Public License for more details. * * You should have received a copy of the GNU General Public License * along with GNU Make; see the file COPYING. If not, write to * the Free Software Foundation, 675 Mass Ave, Cambridge, MA 02139, USA. * */ #include #include "srfft.h" #include "srfftp.h" void fft_8 (complex_t *x); void fft_4(complex_t *x) { /* delta_p = 1 here */ /* x[k] = sum_{i=0..3} x[i] * w^{i*k}, w=e^{-2*pi/4} */ register float yt_r, yt_i, yb_r, yb_i, u_r, u_i, vi_r, vi_i; yt_r = x[0].re; yb_r = yt_r - x[2].re; yt_r += x[2].re; u_r = x[1].re; vi_i = x[3].re - u_r; u_r += x[3].re; u_i = x[1].im; vi_r = u_i - x[3].im; u_i += x[3].im; yt_i = yt_r; yt_i += u_r; x[0].re = yt_i; yt_r -= u_r; x[2].re = yt_r; yt_i = yb_r; yt_i += vi_r; x[1].re = yt_i; yb_r -= vi_r; x[3].re = yb_r; yt_i = x[0].im; yb_i = yt_i - x[2].im; yt_i += x[2].im; yt_r = yt_i; yt_r += u_i; x[0].im = yt_r; yt_i -= u_i; x[2].im = yt_i; yt_r = yb_i; yt_r += vi_i; x[1].im = yt_r; yb_i -= vi_i; x[3].im = yb_i; } void fft_8 (complex_t *x) { /* delta_p = diag{1, sqrt(i)} here */ /* x[k] = sum_{i=0..7} x[i] * w^{i*k}, w=e^{-2*pi/8} */ register float wT1_r, wT1_i, wB1_r, wB1_i, wT2_r, wT2_i, wB2_r, wB2_i; wT1_r = x[1].re; wT1_i = x[1].im; wB1_r = x[3].re; wB1_i = x[3].im; x[1] = x[2]; x[2] = x[4]; x[3] = x[6]; fft_4(&x[0]); /* x[0] x[4] */ wT2_r = x[5].re; wT2_r += x[7].re; wT2_r += wT1_r; wT2_r += wB1_r; wT2_i = wT2_r; wT2_r += x[0].re; wT2_i = x[0].re - wT2_i; x[0].re = wT2_r; x[4].re = wT2_i; wT2_i = x[5].im; wT2_i += x[7].im; wT2_i += wT1_i; wT2_i += wB1_i; wT2_r = wT2_i; wT2_r += x[0].im; wT2_i = x[0].im - wT2_i; x[0].im = wT2_r; x[4].im = wT2_i; /* x[2] x[6] */ wT2_r = x[5].im; wT2_r -= x[7].im; wT2_r += wT1_i; wT2_r -= wB1_i; wT2_i = wT2_r; wT2_r += x[2].re; wT2_i = x[2].re - wT2_i; x[2].re = wT2_r; x[6].re = wT2_i; wT2_i = x[5].re; wT2_i -= x[7].re; wT2_i += wT1_r; wT2_i -= wB1_r; wT2_r = wT2_i; wT2_r += x[2].im; wT2_i = x[2].im - wT2_i; x[2].im = wT2_i; x[6].im = wT2_r; /* x[1] x[5] */ wT2_r = wT1_r; wT2_r += wB1_i; wT2_r -= x[5].re; wT2_r -= x[7].im; wT2_i = wT1_i; wT2_i -= wB1_r; wT2_i -= x[5].im; wT2_i += x[7].re; wB2_r = wT2_r; wB2_r += wT2_i; wT2_i -= wT2_r; wB2_r *= HSQRT2; wT2_i *= HSQRT2; wT2_r = wB2_r; wB2_r += x[1].re; wT2_r = x[1].re - wT2_r; wB2_i = x[5].re; x[1].re = wB2_r; x[5].re = wT2_r; wT2_r = wT2_i; wT2_r += x[1].im; wT2_i = x[1].im - wT2_i; wB2_r = x[5].im; x[1].im = wT2_r; x[5].im = wT2_i; /* x[3] x[7] */ wT1_r -= wB1_i; wT1_i += wB1_r; wB1_r = wB2_i - x[7].im; wB1_i = wB2_r + x[7].re; wT1_r -= wB1_r; wT1_i -= wB1_i; wB1_r = wT1_r + wT1_i; wB1_r *= HSQRT2; wT1_i -= wT1_r; wT1_i *= HSQRT2; wB2_r = x[3].re; wB2_i = wB2_r + wT1_i; wB2_r -= wT1_i; x[3].re = wB2_i; x[7].re = wB2_r; wB2_i = x[3].im; wB2_r = wB2_i + wB1_r; wB2_i -= wB1_r; x[3].im = wB2_i; x[7].im = wB2_r; } void fft_asmb(int k, complex_t *x, complex_t *wTB, const complex_t *d, const complex_t *d_3) { register complex_t *x2k, *x3k, *x4k, *wB; register float a_r, a_i, a1_r, a1_i, u_r, u_i, v_r, v_i; x2k = x + 2 * k; x3k = x2k + 2 * k; x4k = x3k + 2 * k; wB = wTB + 2 * k; TRANSZERO(x[0],x2k[0],x3k[0],x4k[0]); TRANS(x[1],x2k[1],x3k[1],x4k[1],wTB[1],wB[1],d[1],d_3[1]); --k; for(;;) { TRANS(x[2],x2k[2],x3k[2],x4k[2],wTB[2],wB[2],d[2],d_3[2]); TRANS(x[3],x2k[3],x3k[3],x4k[3],wTB[3],wB[3],d[3],d_3[3]); if (!--k) break; x += 2; x2k += 2; x3k += 2; x4k += 2; d += 2; d_3 += 2; wTB += 2; wB += 2; } } void fft_asmb16(complex_t *x, complex_t *wTB) { register float a_r, a_i, a1_r, a1_i, u_r, u_i, v_r, v_i; int k = 2; /* transform x[0], x[8], x[4], x[12] */ TRANSZERO(x[0],x[4],x[8],x[12]); /* transform x[1], x[9], x[5], x[13] */ TRANS(x[1],x[5],x[9],x[13],wTB[1],wTB[5],delta16[1],delta16_3[1]); /* transform x[2], x[10], x[6], x[14] */ TRANSHALF_16(x[2],x[6],x[10],x[14]); /* transform x[3], x[11], x[7], x[15] */ TRANS(x[3],x[7],x[11],x[15],wTB[3],wTB[7],delta16[3],delta16_3[3]); } void fft_64p_c (complex_t *a) { fft_8(&a[0]); fft_4(&a[8]); fft_4(&a[12]); fft_asmb16(&a[0], &a[8]); fft_8(&a[16]), fft_8(&a[24]); fft_asmb(4, &a[0], &a[16],&delta32[0], &delta32_3[0]); fft_8(&a[32]); fft_4(&a[40]); fft_4(&a[44]); fft_asmb16(&a[32], &a[40]); fft_8(&a[48]); fft_4(&a[56]); fft_4(&a[60]); fft_asmb16(&a[48], &a[56]); fft_asmb(8, &a[0], &a[32],&delta64[0], &delta64_3[0]); } void fft_128p_c (complex_t *a) { fft_8(&a[0]); fft_4(&a[8]); fft_4(&a[12]); fft_asmb16(&a[0], &a[8]); fft_8(&a[16]), fft_8(&a[24]); fft_asmb(4, &a[0], &a[16],&delta32[0], &delta32_3[0]); fft_8(&a[32]); fft_4(&a[40]); fft_4(&a[44]); fft_asmb16(&a[32], &a[40]); fft_8(&a[48]); fft_4(&a[56]); fft_4(&a[60]); fft_asmb16(&a[48], &a[56]); fft_asmb(8, &a[0], &a[32],&delta64[0], &delta64_3[0]); fft_8(&a[64]); fft_4(&a[72]); fft_4(&a[76]); /* fft_16(&a[64]); */ fft_asmb16(&a[64], &a[72]); fft_8(&a[80]); fft_8(&a[88]); /* fft_32(&a[64]); */ fft_asmb(4, &a[64], &a[80],&delta32[0], &delta32_3[0]); fft_8(&a[96]); fft_4(&a[104]), fft_4(&a[108]); /* fft_16(&a[96]); */ fft_asmb16(&a[96], &a[104]); fft_8(&a[112]), fft_8(&a[120]); /* fft_32(&a[96]); */ fft_asmb(4, &a[96], &a[112], &delta32[0], &delta32_3[0]); /* fft_128(&a[0]); */ fft_asmb(16, &a[0], &a[64], &delta128[0], &delta128_3[0]); }